Estimation of the Stability of the Machining Technological System Using Nonlinear Dynamics Mathematical Models

2018 ◽  
Author(s):  
A. K. Ostapchuk ◽  
E. M. Kuznetsova ◽  
O. V. Dmitrieva
Keyword(s):  
Nonlinear Dynamics ◽  
Mathematical Models ◽  
Technological System ◽  
The Stability

Diagnostics of the 3D printing process on a CNC machine using machine learning approaches

2021 ◽  
pp. 55-59
Author(s):  
Yu.G. Kabaldin ◽  
D.A. Shatagin ◽  
M.S. Anosov ◽  
P.V. Kolchin ◽  
A.V. Kiselev
Keyword(s):  
Nonlinear Dynamics ◽  
Machine Learning ◽  
3D Printing ◽  
Electric Arc ◽  
Cyber Physical System ◽  
Learning Approaches ◽  
Cnc Machine ◽  
Printing Process ◽  
Optimization Of Process Parameters ◽  
The Stability

Diagnostics and optimization of the dynamics of an electric arc during 3D printing on a CNC machine are considered. The application of nonlinear dynamics methods in assessing the stability of the 3D printing process and the use of artificial neural networks in the classification and optimization of process parameters are shown. Keywords: 3D printing, cyber physical system, machine learning, hybrid processing, neuroform controller, diagnostics, digital twin. [email protected]

scholarly journals Adaptive-Neural-Network-Based Shape Control for a Swarm of Robots

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Xuejing Lan ◽  
Zhenghao Wu ◽  
Wenbiao Xu ◽  
Guiyun Liu
Keyword(s):  
Neural Network ◽  
Nonlinear Dynamics ◽  
Shape Control ◽  
Formation Control ◽  
Adaptive Neural Network ◽  
Multirobot System ◽  
Control Scheme ◽  
Narrow Space ◽  
The Stability ◽  
Unknown Nonlinear Dynamics

This paper considers the region-based formation control for a swarm of robots with unknown nonlinear dynamics and disturbances. An adaptive neural network is designed to approximate the unknown nonlinear dynamics, and the desired formation shape is achieved by designing appropriate potential functions. Moreover, the collision avoidance, velocity consensus, and region tracking are all considered in the controller. The stability of the multirobot system has been demonstrated based on the Lyapunov theorem. Finally, three numerical simulations show the effectiveness of the proposed formation control scheme to deal with the narrow space, loss of robots, and formation merging problems.

scholarly journals The Stability Analyses of the Mathematical Models of Hepatitis C Virus Infection

2015 ◽  
Vol 9 (3) ◽  
Author(s):  
Maureen Siew Fang Chong ◽  
Masitah Shahrill ◽  
Laurie Crossley ◽  
Anotida Madzvamuse
Keyword(s):  
Hepatitis C Virus ◽  
Hepatitis C ◽  
Virus Infection ◽  
Mathematical Models ◽  
Hepatitis C Virus Infection ◽  
Stability Analyses ◽  
The Stability

Numerical Investigation of the Influence of Friction Coefficient on Brake Groan

2010 ◽  
Vol 44-47 ◽  
pp. 1923-1927 ◽  
Author(s):  
Xian Jie Meng
Keyword(s):  
Nonlinear Dynamics ◽  
Friction Coefficient ◽  
Degrees Of Freedom ◽  
Equilibrium Points ◽  
Static Friction ◽  
Kinetic Friction ◽  
Dynamics Model ◽  
Excited Vibration ◽  
Nonlinear Dynamics Model ◽  
The Stability

A two degrees of freedom nonlinear dynamics model of self-excited vibration induced by dry-friction of brake disk and pads is built firstly, the stability of vibration system at the equilibrium points is analyzed using the nonlinear dynamics theory. Finally the numerical method is taken to study the impacts of friction coefficient on brake groan. The calculation result shows that with the increase of kinetic friction coefficient /or the decrease of difference value between static friction coefficient and kinetic friction coefficient can prevent or restrain self-excited vibration from happening.

scholarly journals NECESSITY TO IMPROVE THE MATHEMATICAL MODEL OF FREIGHT CARS TO STUDY CASES OF ITS DERAILMENTS

2020 ◽  
pp. 442-451
Author(s):  
А.V. Batig ◽  
A. Ya. Kuzyshyn
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Computer Experiment ◽  
Rolling Stock ◽  
Software Systems ◽  
Freight Car ◽  
The Stability ◽  
The Many ◽  
The Impact ◽  
The Mathematical Model

One of the most important problems that pose a serious threat to the functioning of railways is the problem of freight cars derailment. However, according to statistics, the number of cases of the derailments of freight cars in trains annually grows. Тo prevent such cases, the necessary preventive measures are developed, and to study the causes of their occurrence, a significant number of mathematical models, programs and software systems created by leading domestic and foreign scientists. Studies of such mathematical models by the authors of this work have led to the conclusion that they are not sufficiently detailed to the extent that it is necessary for analyze the reasons of its derailment. At the same time, an analysis of the causes of the rolling stock derailments on the railways of Ukraine over the past five years showed that in about 20 % of cases they are obvious, and in 7 % of cases they are not obvious and implicitly expressed. The study of such cases of rolling stock derailment during an official investigation by the railway and during forensic railway transport expertises requires the use of an improved mathematical model of a freight car, which would allow a quantitative assessment of the impact of its parameters and rail track on the conditions of railway accidents. Therefore, taking into account the main reasons that caused the occurrence of such railroad accidents over the last five years on the railways of Ukraine, the article selected the main directions for improving the mathematical model of a freight car, allowing to cover all the many factors (explicit and hidden) and identify the most significant ones regarding the circumstances of the derailment rolling stock off the track, established on the basis of a computer experiment. It is proposed in the mathematical model of a freight car to take into account the guiding force, the value of which is one of the main indicators of the stability of the rolling stock. The authors of the article noted that not taking into account the influence of the guiding forces on the dynamics of the freight car can lead to an erroneous determination of the reasons for the rolling stock derailment or even to the impossibility of establishing them.

scholarly journals Application of hybrid asymptotic methods and modern software for mathematical models developing for nonlinear dynamics of structures with variables in time parameters

2021 ◽  
pp. 66-70
Author(s):  
S. Homeniuk ◽  
S. Grebenyuk ◽  
D. Gristchak
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Methods ◽  
Nonlinear Systems ◽  
Analytical Solution ◽  
Mathematical Models ◽  
Nonlinear Dynamic ◽  
Numerical Solutions ◽  
Hybrid Approach ◽  
Time Dependent ◽  
Forced Oscillations

The relevance. The aerospace domain requires studies of mathematical models of nonlinear dynamic structures with time-varying parameters. The aim of the work. To obtain an approximate analytical solution of nonlinear forced oscillations of the designed models with time-dependent parameters. The research methods. A hybrid approach based on perturbation methods, phase integrals, Galorkin orthogonalization criterion is used to obtain solutions. Results. Nonlocal investigation of nonlinear systems behavior is done using results of analytical and numerical methods and developed software. Despite the existence of sufficiently powerful numerical software systems, qualitative analysis of nonlinear systems with variable parameters requires improved mathematical models based on effective analytical, including approximate, solutions, which using numerical methods allow to provide a reliable analysis of the studied structures at the stage designing. An approximate solution in analytical form is obtained with constant coefficients that depend on the initial conditions. Conclusions. The approximate analytical results and direct numerical solutions of the basic equation were compared which showed a sufficient correlation of the obtained analytical solution. The proposed algorithm and program for visualization of a nonlinear dynamic process could be implemented in nonlinear dynamics problems of systems with time-dependent parameters.

Limit Depth of Rock Mine Shafts for Underground Shelters

2017 ◽  
Vol 755 ◽  
pp. 198-201 ◽  
Author(s):  
Alexander N. Kravcov ◽  
Pavel Svoboda ◽  
Vaclav Pospíchal ◽  
Dmitry V. Morozov ◽  
Pavel N. Ivanov
Keyword(s):  
Mathematical Models ◽  
Geological Data ◽  
Power Station ◽  
Rock Property ◽  
Mathematical Properties ◽  
Fallout Shelters ◽  
The Stability ◽  
Selection Of

Today, especially after the several technical accidents, the last one in France Flamanville power station near Cherbour in January 2017 risks of the nuclear hazards due to technical, terrorist or military accidents continually rising. In this situation is of a great importance to start with a retrofit those of underground spaces that was decommissioned in last years and to start thinking about reuse of mining shafts as a fallout shelters for protection of civil population. And the first step is to start with selection of the identify spaces with a mathematical models for selection of the rocks massifs that can be useful for porpoise of the underground shelters. The need to utilise specific geological data, which project organisations usually do not have available. The physical-mathematical properties of rocks are not sufficiently portrayed in these methodologies, which complicates execution of calculations and reduces the credibility of these calculations. The methodology for calculating the stability of rocks around a mine works proposed in the article enables resolution of the task complexly for the conditions of individual deposits, utilising the generalised values of rock property indicators.

scholarly journals Hopf Bifurcation and Dynamic Analysis of an Improved Financial System with Two Delays

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
G. Kai ◽  
W. Zhang ◽  
Z. Jin ◽  
C. Z. Wang
Keyword(s):  
Nonlinear Dynamics ◽  
Hopf Bifurcation ◽  
Equilibrium Point ◽  
Chaotic System ◽  
Financial System ◽  
Two Delays ◽  
Normal Form Method ◽  
The Stability ◽  
Manifold Theory ◽  
Theoretical Results

The complex chaotic dynamics and multistability of financial system are some important problems in micro- and macroeconomic fields. In this paper, we study the influence of two-delay feedback on the nonlinear dynamics behavior of financial system, considering the linear stability of equilibrium point under the condition of single delay and two delays. The system undergoes Hopf bifurcation near the equilibrium point. The stability and bifurcation directions of Hopf bifurcation are studied by using the normal form method and central manifold theory. The theoretical results are verified by numerical simulation. Furthermore, one feature of the proposed financial chaotic system is that its multistability depends extremely on the memristor initial condition and the system parameters. It is shown that the nonlinear dynamics of financial chaotic system can be significantly changed by changing the values of time delays.

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